منابع مشابه
Dual Curves and Pseudoholomorphic Curves
A notion of dual curve for pseudoholomorphic curves in 4–manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with, and yields many analogues of results in complex surface theory, using a description of the local geometry via Cartan’s method of equivalence. Duality then un...
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We show that there exists a real non-singular pseudoholomorphic sextic curve in the affine plane which is not isotopic to any real algebraic sextic curve. This result completes the isotopy classification of real algebraic affine M -curves of degree 6. Comparing this with the isotopy classification of real affine pseudoholomorphic sextic M -curves obtained earlier by the first author, we find th...
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We consider the Taubes correspondencebetween solutions of the Seiberg– Witten equations on a compact 4-dimensional symplectic manifold and pseudoholomorphic curves on this manifold. We compare it with its 3-dimensional analogue in which the roles of Seiberg–Witten equations and pseudoholomorphic curves are played respectively by the Ginzburg–Landau equations and adiabatic paths in the moduli sp...
متن کاملTwistor Theory of Pseudoholomorphic Curves
A twistor theory of pseudoholomorphic curves in 4–manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with, and yields many analogues of results in complex surface theory, using a description of the local geometry via Cartan’s method of equivalence. Twistor theory then un...
متن کاملPseudoholomorphic Curves and the Shadowing Lemma
1. Introduction. Let M be a compact smooth manifold of dimension n, and let T * M → τ M be its cotangent bundle. T * M carries a canonical 1-form θ, which in canonical coordinates (q i , p i) is given by θ = p i dq i. Then ω := dθ is a symplectic form on T * M. To a smooth Hamiltonian H ∈ C ∞ (S 1 ×T * M, R), 1-periodic in time, we associate the Hamiltonian system ˙ x = X H (t, x), (HS) where t...
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2003
ISSN: 1022-1824
DOI: 10.1007/s00029-003-0304-z